Tree
Lateral roots
Lateral roots are roots that spread sideways from the base of a tree, mostly in the top foot or so of soil, often far past the edge of the canopy.
Lateral roots grow outward, not down. Most of a tree's woody roots sit close to the surface, where air and water are best. Arboriculture & Urban Forestry says these roots are predominantly located in the top 30 cm (12 in) of soil and do not normally extend to depths greater than 1 to 2 meters.
The same journal says they grow outward far beyond the branch tips of the tree. This is why one tree can affect a wide area of lawn.
For stumps, the large laterals nearest the trunk are the ones a stump grinder reaches. Iowa State Extension says grinders chew away the stump and any large lateral roots, typically down 8 to 12 inches. Farther out, roots stay put. See surface roots and taproot.